**High School Number Sense Lesson 108: Converting from Base 2 to Base 8**

This concept requires a good understanding of

**BaseNtoBase10**and

**Base10toBaseN**. It appeared

**3 times**this year, with a median placement at

**question # 32**.

**Like our Facebook Page (**

**https://www.facebook.com/numberdojo/**

**) if you want to see new number sense posts on your wall. I will reward you with a free concept index or flashcard file of your choice. Thank you!**

**Number Dojo Level: 305**

Since 8 is a power of 2, we can use a special method of converting from base 2 to base 8.

**How to Solve:**

- Starting at the right, split the base 2 number into
**triples**. - Convert each triple of base 2 numbers into a base 10 number, and write the result down.

**Example 1: 1101 (base 2) = ___ (base 8)**

- We have 2 triples:
**1**and**101** - 1 (base 2) = one 1, which =
**1**(the first digit in the answer) - 101 (base 2) = one 4 + zero 2's + one 1, which =
**5**(the second digit in the answer) - Your answer is
**15**

**Example 2: 11100 (base 2) = ___ (base 8)**

- We have 2 triples:
**11**and**100** - 11 (base 2) = one 2 + one 1, which =
**3**(the first digit in the answer) - 100 (base 2) = one 4 + zero 2's + zero 1's, which =
**4**(the second digit in the answer) - Your answer is
**34**

**Example 3:**

**101111**

_{2}= ____{8}1. We have 2 triples:

**101**and

**111**

2. 101 (base 2) = one 4 + zero 2's + one 1, which =

**5**(the first digit in the answer)

3. 111 (base 2) = one 4 + one 2 + one 1, which =

**7**(the second digit in the answer)

4. Your answer is

**57**

**Example 4:**

**1100101**

_{2}= ____{8}1. We have 3 triples:

**1**,

**100**, and

**101**

2. 1 (base 2) = one 1, which =

**1**(the first digit in the answer)

3. 100 (base 2) = one 4 + zero 2's + zero 1's, which =

**4**(the second digit in the answer)

4. 101 (base 2) = one 4 + zero 2's + one 1, which =

**5**(the third digit in the answer)

5. Your answer is

**145**

**Example 5:**

**10110101**

_{2}= ____{8}1. We have 3 triples:

**10**,

**101**, and

**101**

2. 10 (base 2) = one 2 + zero 1's, which =

**2**(the first digit in the answer)

3. 101 (base 2) = one 4 + zero 2's + one 1, which =

**5**(the second digit in the answer)

4. 101 (base 2) = one 4 + zero 2's + one 1, which =

**5**(the third digit in the answer)

5. Your answer is

**255**

**Up Next for High School: Mult%3**